Worst-Case and Average-Case Hardness of Hypercycle and Database Problems
Abstract
In this paper we present tight lower-bounds and new upper-bounds for hypergraph and database problems. We give tight lower-bounds for finding minimum hypercycles. We give tight lower-bounds for a substantial regime of unweighted hypercycle. We also give a new faster algorithm for longer unweighted hypercycles. We give a worst-case to average-case reduction from detecting a subgraph of a hypergraph in the worst-case to counting subgraphs of hypergraphs in the average-case. We demonstrate two applications of this worst-case to average-case reduction, which result in average-case lower bounds for counting hypercycles in random hypergraphs and queries in average-case databases. Our tight upper and lower bounds for hypercycle detection in the worst-case have immediate implications for the average-case via our worst-case to average-case reductions.
Cite
@article{arxiv.2504.18640,
title = {Worst-Case and Average-Case Hardness of Hypercycle and Database Problems},
author = {Cheng-Hao Fu and Andrea Lincoln and Rene Reyes},
journal= {arXiv preprint arXiv:2504.18640},
year = {2025}
}